Discrete element method modeling of inherently anisotropic rocks under uniaxial compression loading

A new numerical approach is proposed in this study to model the mechanical behaviors of inherently anisotropic rocks in which the rock matrix is represented as bonded particle model, and the intrinsic anisotropy is imposed by replacing any parallel bonds dipping within a certain angle range with smooth‐joint contacts. A series of numerical models with β = 0°, 15°, 30°, 45°, 60°, 75°, and 90° are constructed and tested (β is defined as the angle between the normal of weak layers and the maximum principal stress direction). The effect of smooth‐joint parameters on the uniaxial compression strength and Young's modulus is investigated systematically. The simulation results reveal that the normal strength of smooth‐joint mainly affects the behaviors at high anisotropy angles (β > 45°), while the shear strength plays an important role at medium anisotropy angles (30°–75°). The normal stiffness controls the mechanical behaviors at low anisotropy angles. The angle range of parallel bonds being replaced plays an important role on defining the degree of anisotropy. Step‐by‐step procedures for the calibration of micro parameters are recommended. The numerical model is calibrated to reproduce the behaviors of different anisotropic rocks. Detailed analyses are conducted to investigate the brittle failure process by looking at stress‐strain behaviors, increment of micro cracks, initiation and propagation of fractures. Most of these responses agree well with previous experimental findings and can provide new insights into the micro mechanisms related to the anisotropic deformation and failure behaviors. The numerical approach is then applied to simulate the stress‐induced borehole breakouts in anisotropic rock formations at reduced scale. The effect of rock anisotropy and stress anisotropy can be captured. Copyright © 2015 John Wiley & Sons, Ltd.     

Fluid generation and evolution during exhumation of deeply subducted UHP continental crust: Petrogenesis of composite granite–quartz veins in the Sulu belt,China

Composite granite–quartz veins occur in retrogressed ultrahigh pressure (UHP) eclogite enclosed in gneiss at General's Hill in the central Sulu belt, eastern China. The granite in the veins has a high‐pressure (HP) mineral assemblage of dominantly quartz+phengite+allanite/epidote+garnet that yields pressures of 2.5–2.1 GPa (Si‐in‐phengite barometry) and temperatures of 850–780°C (Ti‐in‐zircon thermometry) at 2.5 GPa (~20°C lower at 2.1 GPa). Zircon overgrowths on inherited cores and new grains of zircon from both components of the composite veins crystallized at c. 221 Ma. This age overlaps the timing of HP retrograde recrystallization dated at 225–215 Ma from multiple localities in the Sulu belt, consistent with the HP conditions retrieved from the granite. The ε_Hf(t) values of new zircon from both components of the composite veins and the Sr–Nd isotope compositions of the granite consistently lie between values for gneiss and eclogite, whereas δ¹⁸O values of new zircon are similar in the veins and the crustal rocks. These data are consistent with zircon growth from a blended fluid generated internally within the gneiss and the eclogite, without any ingress of fluid from an external source. However, at the peak metamorphic pressure, which could have reached 7 GPa, the rocks were likely fluid absent. During initial exhumation under UHP conditions, exsolution of H₂O from nominally anhydrous minerals generated a grain boundary supercritical fluid in both gneiss and eclogite. As exhumation progressed, the volume of fluid increased allowing it to migrate by diffusing porous flow from grain boundaries into channels and drain from the dominant gneiss through the subordinate eclogite. This produced a blended fluid intermediate in its isotope composition between the two end‐members, as recorded by the composite veins. During exhumation from UHP (coesite) eclogite to HP (quartz) eclogite facies conditions, the supercritical fluid evolved by dissolution of the silicate mineral matrix, becoming increasingly solute‐rich, more ‘granitic’ and more viscous until it became trapped. As crystallization began by diffusive loss of H₂O to the host eclogite concomitant with ongoing exhumation of the crust, the trapped supercritical fluid intersected the solvus for the granite–H₂O system, allowing phase separation and formation of the composite granite–quartz veins. Subsequently, during the transition from HP eclogite to amphibolite facies conditions, minor phengite breakdown melting is recorded in both the granite and the gneiss by K‐feldspar+plagioclase+biotite aggregates located around phengite and by K‐feldspar veinlets along grain boundaries. Phase equilibria modelling of the granite indicates that this late‐stage melting records P–T conditions towards the end of the exhumation, with the subsolidus assemblage yielding 0.7–1.1 GPa at <670°C. Thus, the composite granite–quartz veins represent a rare example of a natural system recording how the fluid phase evolved during exhumation of continental crust. The successive availability of different fluid phases attending retrograde metamorphism from UHP eclogite to amphibolite facies conditions will affect the transport of trace elements through the continental crust and the role of these fluids as metasomatic agents interacting with the mantle wedge in the subduction channel.     

Semi‐analytical solution to one‐dimensional consolidation for unsaturated soils with semi‐permeable drainage boundary under time‐dependent loading

This paper presents semi‐analytical solutions to Fredlund and Hasan's one‐dimensional consolidation of unsaturated soils with semi‐permeable drainage boundary under time‐dependent loadings. Two variables are introduced to transform two coupled governing equations of pore‐water and pore‐air pressures into an equivalent set of partial differential equations, which are easily solved by the Laplace transform. The pore‐water pressure, pore‐air pressure and settlement are obtained in the Laplace domain. Crump's method is adopted to perform the inverse Laplace transform in order to obtain semi‐analytical solutions in time domain. It is shown that the present solutions are more general and have a good agreement with the existing solutions from literatures. Furthermore, the current solutions can also be degenerated into conventional solutions to one‐dimensional consolidation of unsaturated soils with homogeneous boundaries. Finally, several numerical examples are provided to illustrate consolidation behavior of unsaturated soils under four types of time‐dependent loadings, including instantaneous loading, ramp loading, exponential loading and sinusoidal loading. Parametric studies are illustrated by variations of pore‐air pressure, pore‐water pressure and settlement at different values of the ratio of air–water permeability coefficient, depth and loading parameters. Copyright © 2017 John Wiley & Sons, Ltd.     

A new bounding surface model for thermal cyclic behaviour

To accurately predict soil volume changes under thermal cycles is of great importance for analysing the performance of many earth structures such as the energy pile and energy storage system. Most of the existing thermo‐mechanical models focus on soil behaviour under monotonic thermal loading only, and they are not able to capture soil volume changes under thermal cycles. In this study, a constitutive model is proposed to simulate volume changes of saturated soil subjected to cyclic heating and cooling. Two surfaces are defined and used: a bounding surface and a memory surface. The bounding surface and memory surface are mainly controlled by the preconsolidation pressure (a function of plastic volumetric strain) and the maximum stress experienced by the soil, respectively. Under thermal cycles, the distance of the two surfaces and plastic modulus increase with an accumulation of plastic strain. By adopting the double surface concept, a new elastoplastic model is derived from an existing single bounding surface thermo‐mechanical model. Comparisons between model predictions and experimental results reveal that the proposed model is able to capture soil volume changes under thermal cycles well. The plastic strain accumulates under thermal cycles, but at a decreasing rate, until stabilization. Copyright © 2017 John Wiley & Sons, Ltd.     

Zircon U–Pb ages and Hf isotope compositions of migmatites from the North Qinling terrane and their geological implications

Migmatites are predominant in the North Qinling (NQ) orogen, but their formation ages are poorly constrained. This paper presents a combined study of cathodoluminescence imaging, U–Pb age, trace element and Hf isotopes of zircon in migmatites from the NQ unit. In the migmatites, most zircon grains occur as new, homogeneous crystals, while some are present as overgrowth rims around inherited cores. Morphological and trace element features suggest that the zircon crystals are metamorphic and formed during partial melting. The inherited cores have oscillatory zoning and yield U–Pb ages of c. 900 Ma, representing their protolith ages. The early Neoproterozoic protoliths probably formed in an active continental margin, being a response to the assembly of the supercontinent Rodinia. The migmatite zircon yields Hf model ages of 1911 ± 20 to 990 ± 22 Ma, indicating that the protoliths were derived from reworking of Palaeoproterozoic to Neoproterozoic crustal materials. The anatexis zircon yields formation ages ranging from 455 ± 5 to 420 ± 4 Ma, with a peak at c. 435 Ma. Combined with previous results, we suggest that the migmatization of the NQ terrane occurred at c. 455–400 Ma. The migmatization was c. 50 Ma later than the c. 490 Ma ultra‐high‐P (UHP) metamorphism, indicating that they occurred in two independent tectonic events. By contrast, the migmatization was coeval with the granulite facies metamorphism and the granitic magmatism in the NQ unit, which collectively argue for their formation due to the northward subduction of the Shangdan Ocean. UHP rocks were distributed mainly along the northern margin and occasionally in the inner part of the NQ unit, indicating that they were exhumed along the northern edge and detached from the basement by the subsequent migmatization process.     

Elastic lateral dynamic impedance functions for a rigid cylindrical shell type foundation

Elastic lateral dynamic impedance functions are defined as the ratio of the lateral dynamic force/moment to the corresponding lateral displacement/rotation at the top ending of a foundation at very small strains. Elastic lateral dynamic impedance functions have a defining influence on the natural frequencies of offshore wind turbines supported on cylindrical shell type foundations, such as suction caissons, bucket foundations, and monopiles. This paper considers the coupled horizontal and rocking vibration of a cylindrical shell type foundation embedded in a fully saturated poroelastic seabed in contact with a seawater half‐space. The formulation of the coupled seawater–shell–seabed vibration problem is simplified by treating the shell as a rigid one. The rigid shell vibration problem is approached by the integral equation method using ring‐load Green's functions for a layered seawater‐seabed half‐space. By considering the boundary conditions at the shell–soil interface, the shell vibration problem is reduced to Fredholm integral equations. Through an analysis of the corresponding Cauchy singular equations, the intrinsic singular characteristics of the problem are rendered explicit. With the singularities incorporated into the solution representation, an effective numerical method involving Gauss–Chebyshev method is developed for the governing Fredholm equations. Selected numerical results for the dynamic contact load distributions, displacements of the shell, and lateral dynamic impedance functions are examined for different shell length–radius ratio, poroelastic materials, and frequencies of excitation. Copyright © 2016 John Wiley & Sons, Ltd.